NYU is famously stingy with financial aid.
Most US colleges don’t give financial aid to international students (or, if they do, are less likely to accept internationals applying for FA) and so you would likely be looking at full tuition + room and board + various costs (texbooks, public transport, etc), for a total of about $60K a year. Over 4 years, that’s nearly a quarter of a million dollars. If you can get into a good UK school, that’s probably a better deal, and you can always get a Master’s degree from a US school (employers don’t usually care about your undergrad college anyway).